Next, we derive the representations of \(\phi \) , \(u\) , and \(\rho \)  in terms of the Riemann theta
function. A special case of Riemann's vanishing theorem (cf. Theorem A.26 [1]})
yields
\(\theta (\underline{\Xi }_{Q_0}-\underline{A}_{Q_0}(P)+\underline{\alpha }_{Q_0}(\mathcal {D}_{\underline{Q}}))=0 \quad \textrm { if and only if P\in \lbrace Q_1,\ldots ,Q_n\rbrace }.\) 
